High-quality image resizing using oblique projection operators

New Efficient Interpolation Techniques for Medical Images.. [DOI: 10.21203/rs.3.rs-2869416/v1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

This paper presents new efficient six image interpolation techniques that aim to obtain high resolution images from low resolution ones. The problem of dealing with image interpolation as an inverse problem was treated in wavelet domain through the first proposed approach. This approach estimates wavelet coefficients in high frequency sub-images using least squares algorithm. The approach reveals performance improvement in PSNR and MSE values compared to bilinear and least squares algorithm. A second approach based on using artificial neural network for modeling the maximum entropy interpolation algorithm was presented. Training the suggested network is achieved by adjusting its weights using learning algorithm to minimize the sum of squared error between target and actual output of output neurons. The proposed approach requires fewer computations than the conventional high-quality image interpolation methods with little reduction in PSNR compared to the maximum entropy algorithm. A third algorithm which combines new contourlet transform and edge-based interpolation algorithm was proposed to improve object boundaries regularity which could be achieved by treating each successive approximation of the high-resolution image as a noisy approximation, hence enforcing the contourlet coefficients to have a sparsity constraint. The proposed algorithm gives an improvement of 2 dB in PSNR compared to IIGR algorithm and achieves the best MSE and correlation coefficient. The fourth approach presents an efficient method to get HR images from the fusion of Magnetic resonance and computed tomography images by adopting least-squares strategy to iteratively obtain wavelet sub-bands of the target HR image. The proposed approach was found to achieve good results especially when the curvelet transform is used to merge the CT and MR images. The fifth approach presents neural modeling of the maximum entropy image interpolation algorithm based on both curvelet and wavelet fusion. Through this approach the fusion process is performed while edges with a curved nature are preserved. Results showed that applying curvelet transform in the fusion of CT and MR images is better than DWT fusion and that interpolating the fused image by neural modeling of maximum entropy image interpolation algorithm is superior to interpolating the original MR and CT images. The sixth approach presents a new image scale-up, super-resolution, approach based on image fusion principle. MR and CT images were scaled-up using sparse-representation modeling with dictionary learning algorithms of Yang et. al. and Michael et. al.. The images were fused by discrete wavelet and curvelet transforms, then scaled-up by the same algorithms. Simulation results showed that scaling-up the fused MR and CT images, either by wavelet or curvelet fusion techniques, gives higher PSNR values than scaling-up the MR and CT image separately.

Exact gram filtering and efficient back projection for iterative CT reconstruction

PURPOSE

Forward and back-projections are the basis of all model-based iterative reconstruction (MBIR) methods. However, computing these accurately is time consuming. In this paper, we present a method for model-based iterative reconstruction in parallel X-ray beam geometry that utilizes a Gram filter to efficiently implement forward and back projection.

METHODS

We propose using voxel-basis and modeling its footprint in a box spline framework to calculate the Gram filter exactly and improve the performance of back-projection. In the special case of parallel X-ray beam geometry, the forward and back-projection can be implemented by an estimated Gram filter efficiently if the sinogram signal is bandlimited. In this paper, a specialized sinogram interpolation method is proposed to eliminate the bandlimited prerequisite and thus improve the reconstruction accuracy. We build on this idea by utilizing the continuity of the voxel-basis' footprint, which provides a more accurate sinogram interpolation and further improves the efficiency and quality of back-projection. In addition, the detector blur effect can be efficiently accounted for in our method to better handle realistic scenarios.

RESULTS

The proposed method is tested on both phantom and real CT images under different resolutions, sinogram sampling steps, and noise levels. The proposed method consistently outperforms other state-of-the-art projection models in terms of speed and accuracy for both back-projection and reconstruction.

CONCLUSIONS

We proposed a iterative reconstruction methodology for 3D parallel-beam X-ray CT reconstruction. Our experimental results demonstrate that the proposed methodology is accurate, fast, and reproducible, and outperforms alternative state-of-the-art projection models on both back-projection and reconstruction results significantly. This article is protected by copyright. All rights reserved.

Medical Image Magnification Based on Original and Estimated Pixel Selection Models

BACKGROUND

The issue of medial image resolution enhancement is one of the most important topics for medical imaging that helps improve the performance of many post-processing aspects like classification and segmentation towards medical diagnosis.

OBJECTIVE

Our aim in this paper is to evaluate different types of pixel selection models in terms of pixel originality in medical image reconstruction problems. A previous investigation showed that selecting far original pixels has highly better performance than using near unoriginal/estimated pixels while magnifying some benchmarks in digital image processing.

MATERIAL AND METHODS

In our technical study, we apply two classical interpolators, cubic convolution (CC) and bi-linear (BL), in order to reconstruct medical images in spatial domain. In addition to the interpolators, we use some geometrical image transforms for creating the reconstruction models.

RESULTS

The results clearly demonstrate that despite the absolute preference of the original pixel selection model in the first research, we cannot see this preference in medical dataset in which the results of BL interpolator for both tested models (original and estimated pixel selection models) are approximately the same as each other and for CC interpolator, we only see a relatively better preference for the original pixel selection model.

CONCLUSION

The current research reveals the fact that selection models are not a general factor in reconstruction problems, and the structure of the basic interpolators is also a main factor which affects the final results. In other words, some interpolators in medical dataset can be affected by the selection models, while, some cannot.

High-Quality Parallel-Ray X-Ray CT Back Projection Using Optimized Interpolation

We propose a new, cost-efficient method for computing back projections in parallel-ray X-ray CT. Forward and back projections are the basis of almost all X-ray CT reconstruction methods, but computing these accurately is costly. In the special case of parallel-ray geometry, it turns out that reconstruction requires back projection only. One approach to accelerate the back projection is through interpolation: fit a continuous representation to samples of the desired signal, then sample it at the required locations. Instead, we propose applying a prefilter that has the effect of orthogonally projecting the underlying signal onto the space spanned by the interpolator, which can significantly improve the quality of the interpolation. We then build on this idea by using oblique projection, which simplifies the computation while giving effectively the same improvement in quality. Our experiments on analytical phantoms show that this refinement can improve the reconstruction quality for both filtered back projection and iterative reconstruction in the high-quality regime, i.e., with low noise and many measurements.

Viewing-distance aware super-resolution for high-definition display

In this paper, we propose a novel algorithm for high-definition displays to enlarge low-resolution images while maintaining perceptual constancy (i.e., the same field-of-view, perceptual blur radius, and the retinal image size in viewer's eyes). We model the relationship between a viewer and a display by considering two main aspects of visual perception, i.e., scaling factor and perceptual blur radius. As long as we enlarge an image while adjust its image blur levels on the display, we can maintain viewer's perceptual constancy. We show that the scaling factor should be set in proportion to the viewing distance and the blur levels on the display should be adjusted according to the focal length of a viewer. Toward this, we first refer to edge directions to interpolate a low-resolution image with the increasing of viewing distance and the scaling factor. After images are interpolated, we utilize a local contrast to estimate the spatially varying image blur levels of the interpolated image. We then further adjust the image blur levels using a parametric deblurring method, which combines L1 as well as L2 reconstruction errors, and Tikhonov with total variation regularization terms. By taking these factors into account, high-resolution images adaptive to viewing distance on a display can be generated. Experimental results on both natural image metric and user subjective studies across image scales demonstrate that the proposed super-resolution algorithm for high-definition displays performs favorably against the state-of-the-art methods.

A CORRELATIVE TWO-STEP APPROACH TO HALLUCINATING FACES

Face hallucination is to synthesize high-resolution face image from the input low-resolution one. Although many two-step learning-based face hallucination approaches have been developed, they suffer from the expensive computational cost due to the separate calculation of the global and local models. To overcome this problem, we propose a correlative two-step learning-based face hallucination approach which bridges the gap between the global model and the local model. In the global phase, we build a global face hallucination framework by combining the steerable pyramid decomposition and the reconstruction. In the residue compensation phase, based on the combination weights and constituent samples obtained in the global phase, a residue face image is synthesized by the neighbor reconstruction algorithm to compensate the hallucinated global face image with subtle facial features. The ultimate hallucinated result is synthesized by adding the residue face image to the global face image. Compared with existing methods, in the global phase, our global face image is more similar to the original high-resolution face image. Furthermore, in the residue compensation phase, we use the combination weights and constituent samples obtained in the global phase to compute the residue face image, by which the computational efficiency can be greatly improved without compromising the quality of facial details. The experimental results and comparisons demonstrate that our approach can not only generate convincible high-resolution face images efficiently, but also has high computational efficiency. Furthermore, our proposed approach can be used to restore the damaged face images in image inpainting. The efficacy of our approach is validated by recovering the damaged face images with visually good results.

Curvature interpolation method for image zooming

We introduce a novel image zooming algorithm, called the curvature interpolation method (CIM), which is partial-differential-equation (PDE)-based and easy to implement. In order to minimize artifacts arising in image interpolation such as image blur and the checkerboard effect, the CIM first evaluates the curvature of the low-resolution image. After interpolating the curvature to the high-resolution image domain, the CIM constructs the high-resolution image by solving a linearized curvature equation, incorporating the interpolated curvature as an explicit driving force. It has been numerically verified that the new zooming method can produce clear images of sharp edges which are already denoised and superior to those obtained from linear methods and PDE-based methods of no curvature information. Various results are given to prove effectiveness and reliability of the new method.

Color image resolution conversion

In this paper, we look at the problem of spatially scaling color images. We focus on an approach that takes advantage of the human visual system's color spatial frequency sensitivity. The algorithm performs an efficient least-squares (LS) resolution conversion for the luminance channel and a low-complexity pixel replication/reduction in the chrominance channels. The performance of the algorithm is compared to a LS method in sRGB and CIELAB color spaces, as well as standard bilinear interpolation in sRGB space. The comparisons are made in terms of computational cost and color error in sCIELAB.

Adaptively quadratic (AQua) image interpolation

Image interpolation is a key aspect of digital image processing. This paper presents a novel interpolation method based on optimal recovery and adaptively determining the quadratic signal class from the local image behavior. The advantages of the new interpolation method are the ability to interpolate directly by any factor and to model properties of the data acquisition system into the algorithm itself. Through comparisons with other algorithms it is shown that the new interpolation is not only mathematically optimal with respect to the underlying image model, but visually it is very efficient at reducing jagged edges, a place where most other interpolation algorithms fail.

Least-squares image resizing using finite differences

We present an optimal spline-based algorithm for the enlargement or reduction of digital images with arbitrary (noninteger) scaling factors. This projection-based approach can be realized thanks to a new finite difference method that allows the computation of inner products with analysis functions that are B-splines of any degree n. A noteworthy property of the algorithm is that the computational complexity per pixel does not depend on the scaling factor a. For a given choice of basis functions, the results of our method are consistently better than those of the standard interpolation procedure; the present scheme achieves a reduction of artifacts such as aliasing and blocking and a significant improvement of the signal-to-noise ratio. The method can be generalized to include other classes of piecewise polynomial functions, expressed as linear combinations of B-splines and their derivatives.

Survey: interpolation methods in medical image processing

Image interpolation techniques often are required in medical imaging for image generation (e.g., discrete back projection for inverse Radon transform) and processing such as compression or resampling. Since the ideal interpolation function spatially is unlimited, several interpolation kernels of finite size have been introduced. This paper compares 1) truncated and windowed sinc; 2) nearest neighbor; 3) linear; 4) quadratic; 5) cubic B-spline; 6) cubic; g) Lagrange; and 7) Gaussian interpolation and approximation techniques with kernel sizes from 1 x 1 up to 8 x 8. The comparison is done by: 1) spatial and Fourier analyses; 2) computational complexity as well as runtime evaluations; and 3) qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing. For local and Fourier analyses, a standardized notation is introduced and fundamental properties of interpolators are derived. Successful methods should be direct current (DC)-constant and interpolators rather than DC-inconstant or approximators. Each method's parameters are tuned with respect to those properties. This results in three novel kernels, which are introduced in this paper and proven to be within the best choices for medical image interpolation: the 6 x 6 Blackman-Harris windowed sinc interpolator, and the C2-continuous cubic kernels with N = 6 and N = 8 supporting points. For quantitative error evaluations, a set of 50 direct digital X rays was used. They have been selected arbitrarily from clinical routine. In general, large kernel sizes were found to be superior to small interpolation masks. Except for truncated sinc interpolators, all kernels with N = 6 or larger sizes perform significantly better than N = 2 or N = 3 point methods (p << 0.005). However, the differences within the group of large-sized kernels were not significant. Summarizing the results, the cubic 6 x 6 interpolator with continuous second derivatives, as defined in (24), can be recommended for most common interpolation tasks. It appears to be the fastest six-point kernel to implement computationally. It provides eminent local and Fourier properties, is easy to implement, and has only small errors. The same characteristics apply to B-spline interpolation, but the 6 x 6 cubic avoids the intrinsic border effects produced by the B-spline technique. However, the goal of this study was not to determine an overall best method, but to present a comprehensive catalogue of methods in a uniform terminology, to define general properties and requirements of local techniques, and to enable the reader to select that method which is optimal for his specific application in medical imaging.